Practice Case Studies And Problems (4.1.8) - Continuity Equations - Fluid Mechanics

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6 sample questions

Question 1.
Define the continuity equation.
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Think about mass flow.
Question 2.
What is divergence in fluid mechanics?
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Consider vector fields.
3Question 3.
What does the continuity equation express?
- Mass conservation
- Energy conservation
- Momentum conservation
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Think about the principle of mass flow.
4Question 4.
True or False: Incompressible flow assumes density varies with pressure.
- True
- False
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Reflect on the definitions of incompressible flow.
Question 5.
Consider a cylindrical tank with a piston compressing air. If the piston moves at a speed of 0.1 m/s, calculate how the density changes with time if initially, the density is known.
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Account for changes in the volume and apply the continuity equation.
Question 6.
Given a two-dimensional flow field represented as v(x,y) = (x, y^2), determine if the flow is incompressible or not.
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Remember to differentiate with respect to each variable and sum them.

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